Example: A single square loop of wire with a resistance of 100  and 10 cm long sides is rotated from 30 o to 60 o in a constant magnetic field of 5T. Determine the average current induced in the loop during a 10 s interval. A 1 The increasing angle decreases the area of the loop that the magnetic field passes through. Change d to  because we are looking at large changes, not infinitesimal changes.

We have so far focused on determining the magnitude of the induced voltage and hence the magnitude of the induced current in a loop. We must also determine the direction of the current in this loop. We can determine the direction of the induced current using Lenz’s Law. We know from Faraday’s Law that the induced voltage (and induced current) oppose the change in the magnetic flux. B increasing B decreasing B induced I induced For descriptive purposes let use a changing magnetic field to represent the changing flux. Remember Lenz’s Law refers to a changing flux! An increasing magnetic field can be visualized as a vector with increasing length. The loop will resist the changing magnetic field. (Try to keep the vector the same length) This can be done by inducing a current that generates a magnetic field that points in the opposite direction to the increasing magnetic field. We call this the induced magnetic field. Using the second right-hand rule we can determine the direction of the induced current from our knowledge of the direction of the induced magnetic field.

A long, straight wire carries a steady current I. A rectangular conducting loop lies in the same plane as the wire, with two sides parallel to the wire and two sides perpendicular. Suppose the loop is pushed toward the wire as shown. Given the direction of I, the induced current in the loop is 1. clockwise. 2. counterclockwise. 3. need more information B increases as you approach the long straight wire.

The photograph at the left below shows a ramp leading into the gap of a fairly strong permanent magnet. If a wooden dowel rod is rolled down the ramp, what will happen when it rolls into the magnet gap? Now suppose that the four tubes in the photograph at the right above: aluminum, copper, iron, and plastic respectively, are rolled down the ramp into the magnet gap. What will happen in each case? In particular, how quickly will they reach the end of the ramp? Rank the four rods in order of how fast they reach the end of the ramp, with the faster rod first. (1) aluminum.aluminum (2) copper.copper (3) iron.iron (4) plastic.plastic The answer is "nothing;" wood is not attracted by magnets, at least not on the scale of this experiment. Fastest Slowest Medium

Faraday’s Law provides a relationship between voltage and magnetic flux. We know that voltage is related to the electric field. Therefore we should be able to relate the electric field to the magnetic flux. General form of Faraday’s Law (One of Maxwell’s Equations) We use a closed integral here since we are looking at the flow of charge in an electric circuit. Generators and Motors Generators and motors are applications of Faraday’s Law. What does a generator do? What does a motor do? Converts mechanical energy to electrical energy. Converts electrical energy to mechanical energy.

When the coil is rotated within an external magnetic field the effective area of the loop that the magnetic field passes through changes from a maximum flux (A and B are parallel) to a minimum (zero) flux (A and B are perpendicular). What is the direction of the current when the angle of the loop is rotated from 0 o to 90 o ? What is the direction of the current when the angle of the loop is rotated from 90 o to 180 o ? Clockwise – The magnetic flux is decreasing in time. Counterclockwise – The magnetic flux is increasing in time. This gives what we call an alternating current. To generate a direct current you use a cylindrical ring with a gap that switches the connector directions as the loop rotates. Types of Generators Turbine (wind, steam, water) Diesel Nuclear Reactor (also a turbine) Magneto hydrodynamic Types of Motors Electric Turbine (air jet, water jet) Magneto hydrodynamic – only works for very small masses (grams)